For a fixed domain \(\Omega \) , several papers have studied what analytic subvarieties gave rise to np pairs [1]}, [2]}, [3]}, [4]}, [5]}. If \(\Omega \)  is suitably nice, the conclusion of these papers was that \(V\)  had to be a holomorphic retract of \(\Omega \)  for \((\Omega ,V)\)  to be an np pair.
However, this is not true in general. The simplest example is the np pair \((\Delta ,T)\) ,
where \(\Delta \)  is the diamond
\(\lbrace z\in \mathbb {C}^2:\ |z_1|+|z_2|<1\rbrace \) , and \(T =(\mathbb {D}\times \lbrace 0\rbrace )\cup (\lbrace 0\rbrace \times \mathbb {D})\) .
